Celebratio Mathematica

James M. Kister

James Milton Kister

by Rob Kirby

James M. Kister was born on 29 June 1930 in Clev­e­land, Ohio to James Le­onard Kister and Kath­er­ine Sher­rick Kister. Jim’s pa­ternal grand­fath­er came to Ohio from Pennsylvania in 1840, found land with a stream; built a dam, wa­ter­wheel and mill; and then ground wheat and corn and made cider.

Jim’s fath­er, JLK, did not fin­ish high school, but had a tal­ent with ma­chinery. In 1908 his fath­er bought a car in Chica­go, which was then dis­as­sembled, boxed, and shipped by train to Mill­brook, Ohio (named for the Kister mill). JLK and his fath­er took a buggy to the train sta­tion where JLK re­as­sembled the car and drove it home! (That seems an odd way to get a car from Chica­go to Ohio, even in 1908.) JLK went on to work as an in­spect­or of cars and trucks for White Mo­tor Com­pany (later bought by Mack) in Clev­e­land.

Jim lived in Clev­e­land through high school, win­ning prizes in math and phys­ics. He went to Woost­er Col­lege (Ohio) from 1948–52, win­ning the Rens­selaer Prize in math. Melch­er Fobes, a Hassler Whit­ney stu­dent at the time, was the main math teach­er at Woost­er, and en­cour­aged Jim to go to Har­vard for gradu­ate work.

Jim star­ted well at Har­vard in 1952, but fell ill with a lung in­fec­tion and had to leave Har­vard be­fore Thanks­giv­ing and go to live in Tuc­son for its drier air. After a few months Los Alam­os called with a job of­fer (George Birk­hoff helped). Jim worked there for al­most two years, with a three month break when the lower lobe of his left lung was re­moved.

On the ad­vice of Stan­islaw Ulam and C. J. Ever­ett, and for the bet­ter air, Jim began gradu­ate school at the Uni­versity of Wis­con­sin in Madis­on in fall, 1955. That semester Jim took a point set to­po­logy course from Bob Wil­li­ams (a Gor­don Why­burn Ph.D. at the Uni­versity of Vir­gin­ia) and this got Jim in­ter­ested in to­po­logy.

Jim met Sue Spence in sum­mer 1955. They were mar­ried in 1956 and daugh­ter Kar­en was born in Decem­ber 1957. A Wis­con­sin fel­low­ship only paid \$1500 so the young couple went to Los Alam­os in sum­mer 1956 to make ex­tra money.

Ulam wanted Jim to join his team to work on a chess play­ing pro­gram. This seemed too for­mid­able so the chess board was shrunk to \( 6 \times 6 \) and the rooks were elim­in­ated. They wrote a pro­gram and got a good chess play­er, Mar­tin Kruskal, to test the pro­gram. Kruskal spot­ted the pro­gram a queen, and then did not have an easy time beat­ing it. Jim gave a talk on the chess play­ing pro­gram be­fore a large audi­ence at a meet­ing of the As­so­ci­ation for Com­put­ing Ma­chinery in Los Angeles, and pub­lished a pa­per [1]. A couple of courses from R H Bing in 1956–57 led to Bing be­com­ing Jim’s Ph.D. ad­visor. Bing was away at the In­sti­tute for Ad­vanced Study in 1957–58 and when he re­turned he sug­ges­ted that Jim work on the Side Ap­prox­im­a­tion The­or­em (later proved by Bing [e4]). In­stead Jim, in early 1959, saw that the space of bounded homeo­morph­isms (with the com­pact-open to­po­logy) of \( \mathbb{R}^n \) is con­tract­ible, for any \( n \). (Bounded means that there is some con­stant \( K \) such that the homeo­morph­ism does not move any point more than dis­tance \( K \).) The proof took one page, and can be seen as a ca­non­ic­al ver­sion of the Al­ex­an­der iso­topy [e1] which shows that a homeo­morph­ism of the \( n \)-ball, \( B^n \), which is equal to the iden­tity on the bound­ing \( (n-1) \)-sphere, is iso­top­ic to the iden­tity. Jim saw that if one squeezes the homeo­morph­ism of \( \mathbb{R}^n \) in­to a homeo­morph­ism of \( B^n \), then it will be equal to the iden­tity on the bound­ary. In his Math Re­view, S. S. Cairns called the proof “re­mark­ably ef­fi­cient”, which it cer­tainly is.

Bing re­portedly asked the au­thor­it­ies wheth­er the Uni­versity would ac­cept a one page thes­is for a Ph.D. The an­swer is un­known and ir­rel­ev­ant for Jim also at the same time proved that the space of homeo­morph­isms of a 3-man­i­fold is loc­ally con­nec­ted [2]. Jim put his bounded homeo­morph­isms the­or­em in­to [2], which had 3-man­i­folds in the title, but no men­tion of high­er di­men­sions. That led to my over­look­ing the res­ult for many dec­ades, and led me to cite in­stead a pa­per of Ed Con­nell [e5] in my pa­per [e7] us­ing the tor­us trick to prove loc­al con­tract­ib­il­ity for all homeo­morph­isms (not just bounded) of \( \mathbb{R}^n \). Jim’s res­ult is key to my the­or­em, and it’s em­bar­rass­ing that my ac­quaint­ances and I didn’t know of its ex­ist­ence!

In 1963 Jim proved a very im­port­ant the­or­em, that a to­po­lo­gic­al man­i­fold has a tan­gent bundle [6]. Mil­nor had defined the no­tion of a mi­crobundle and showed that mi­crobundles had many of the use­ful prop­er­ties of ac­tu­al bundles [e6]. Jim showed that every mi­crobundle (over a loc­ally fi­nite, fi­nite di­men­sion­al com­plex) con­tains a bundle (with fiber \( \mathbb{R}^n \) and group equal to the space of homeo­morph­isms of \( \mathbb{R}^n \) with the com­pact open to­po­logy). The key to the proof is the the­or­em stat­ing that the space of homeo­morph­isms of \( \mathbb{R}^n \) is a weak de­form­a­tion re­tract of the space of em­bed­dings of \( \mathbb{R}^n \) in­to \( \mathbb{R}^n \).

Ker­vaire called the proof, “ele­ment­ary but del­ic­ate”, in his Math Re­view, which is ac­cur­ate but misses the fact that many geo­met­ric proofs from that era looked ele­ment­ary, but only after the fact.

If \( T \) is a homeo­morph­ism of peri­od \( r \) on Eu­c­lidean space \( E^n \), then P. A. Smith [e2] proved that \( T \) has a fixed point if \( r \) is prime or a prime power. Then Con­ner and Floyd [e3] gave ex­amples when \( r \) is not a prime power of con­tract­ible spaces with peri­od­ic maps with no fixed points.

Jim wrote two pa­pers [3] [5] giv­ing counter­examples for all \( r \) which are not prime powers. The second pa­per con­structs a map on a con­tract­ible in­fin­ite com­plex \( K \) which is then em­bed­ded equivari­antly in \( E^n \) for \( n > 7 \), and then a reg­u­lar neigh­bor­hood of \( K \) is the de­sired Eu­c­lidean space. The map can be made dif­fer­en­ti­able, and these ex­amples are nearly best pos­sible, the only case left open was \( n=7 \). The case \( n=7 \) has been settled: R. Oliv­er an­nounced fixed point free maps in [No­tices of the AMS, 26 (1979), no. 2, A251], but de­tails were nev­er pub­lished. In [e8] the four au­thors give the rel­ev­ant de­tails of the \( n=7 \) proof.

Jim and Russ Mc­Mil­lan con­struc­ted [4] a con­tract­ible open man­i­fold \( M \) which can­not be em­bed­ded in \( E^3 \). All pre­vi­ous such ex­amples were em­bed­dable in \( E^3 \). However, \( M \times E^1 \) and \( E^4 \) are com­bin­at­or­i­ally equi­val­ent.

While on sab­bat­ic­al at Ox­ford Uni­versity in 1977, Jim met Jane Bridge, a math­em­at­ic­al lo­gi­cian, ten­ured at Somerville Col­lege of Ox­ford Uni­versity. She was a stu­dent of Robin Gandy and thus a grand­daugh­ter of Alan Tur­ing. Jane and Jim were mar­ried in 1978 and re­turned to Ann Ar­bor where Jane be­came an ed­it­or of Math Re­views. In 1998 she be­came the Ex­ec­ut­ive Dir­ect­or of MR.

I met Jim in 1966–67 when he spent a year at UCLA. He gave a course on to­po­lo­gic­al bundles and his notes from that course and my notes from a course two years later on tri­an­gu­la­tions of to­po­lo­gic­al man­i­folds led us to plan a book to­geth­er. Fin­ish­ing this book kept get­ting put off — even though it is now 90% done. It should have been fin­ished be­fore Jim died, and will be soon.

Jim was a very good friend, a good ath­lete (des­pite be­ing plagued by bron­chiectas­is all his life) and in par­tic­u­lar was a cagey ten­nis play­er.


[1] J. Kister, P. Stein, S. Ulam, W. Walden, and M. Wells: “Ex­per­i­ments in chess,” Jour. As­soc. Com­put­ing Ma­chinery 4 (1957), pp. 174–​177. article

[2] J. Kister: “Small iso­top­ies in Eu­c­lidean spaces and 3-man­i­folds,” Bull. Am. Math. Soc. 65 : 6 (1959), pp. 371–​373. MR 107232 Zbl 0089.​39502 article

[3] J. M. Kister: “Ex­amples of peri­od­ic maps on Eu­c­lidean spaces without fixed points,” Bull. Am. Math. Soc. 67 : 5 (1961), pp. 471–​474. MR 130929 Zbl 0101.​15602 article

[4] J. M. Kister and D. R. Mc­Mil­lan, Jr.: “Loc­ally eu­c­lidean factors of \( E^4 \) which can­not be im­bed­ded in \( E^3 \),” Ann. Math. (2) 76 : 3 (November 1962), pp. 541–​546. MR 144322 Zbl 0115.​40703 article

[5] J. M. Kister: “Dif­fer­en­ti­able peri­od­ic ac­tions on \( E^8 \) without fixed points,” Am. J. Math. 85 : 2 (April 1963), pp. 316–​319. MR 154278 Zbl 0119.​18801 article

[6]J. M. Kister: “Mi­crobundles are fibre bundles,” Ann. of Math. (2) 80 (1964), pp. 190–​199. MR 0180986 Zbl 0131.​20602 article

[7] J. Chee­ger and J. M. Kister: “Count­ing to­po­lo­gic­al man­i­folds,” To­po­logy 9 : 2 (May 1970), pp. 149–​151. MR 256399 Zbl 0199.​58403 article